To estimate the rate for optimization, following  [1]}, [2]}, the latent \(\hat{y}_i\)  is modeled as a Gaussian convolved with a unit uniform distribution to ensure a good match between the actual discrete entropy and the continuous entropy model used during training. Then the distribution of latent is modeled by predicting the mean and scale parameters conditioned on the quantized hyperprior \(\hat{z}\)  and causal context of each latent element \(\hat{y}_{<i}\)  (e.g., left and upper latent elements).
